Question

1)What is the domain of f/g?
f(x) = x/x+1, g(x) = x^3

all real numbers greater than 1. Am I correct?

2) Find f x g, g x f, and f x f

f(x) = 3sqrt x-1 g(x) = x^3+1
For the f(x) the 3 is little above the sqrt sign.

I do not understand how do fidn these.

Answer 1

(1) Not quite, you need to exclude cases where the denominator becomes zero, where the function is undefined.

For f(x), the domain is R for the numerator, and R\-1 for the denominator, since x+1 cannot equal zero as a denominator. In all dom f(x) is R\-1.
For g(x), the domain is simply R.
For f/g, g(x) cannot be zero, so dom g(x) = R\-1,0
The combined domain of f(x)/g(x) is therefore R\0,1, or in interval notation: (-∞,0)∪(0,1)∪(1,∞).